Investigation of Localized Induction Approximation in Vortex Reconnection

Abstract

In general, the vortex motion is described by the Biot-Savart law. Furthermore, under the localized induction approximation (LIA), the curvature and induced velocity of vortex are proportional, and then the vortex motion is described by the nonlinear Schrödinger equation. In this study, we focused on the vortex reconnection, which is one of the vortex interactions. In the reconnection problem of two vortex rings, by numerically analyzing the relationship between the curvature and induced velocity along the vortex ring, it was investigated at which location of the vortex ring the LIA held and at which location the LIA did not hold. The results helped a theoretical understanding of the reconnection.